Max Acceleration from Friction w/ Coeff 0.95: 9.3 m/s2

[tmobilerocks]

Homework Statement

What is the greatest acceleration that can be generated by a runner if the coefficient of static friction between shoes and road is 0.95?

Homework Equations

Fnet = ma
Force of static friction: u_sN
Weight= mg

The Attempt at a Solution

FBD: Positive x-axis is to the right. Positive y-axis is to the top. Normal force pointing up, equal in magnitude to weight pointing down. Friction must point in the positive x direction.

f = ma_x
a_x = u_sg
a_max = (0.95*9.81)
= 9.3 m/s²

I just have one question. Does the friction force point to the right, in the direction of the positive x axis? Thanks!

 

[BvU]

To answer your one question yourself you can imagine trying to accelerate on an (almost) friction-free surface, such as ice.

 

[tmobilerocks]

So the friction force would point to the right? Due to Fnet = ma, the acceleration and net force should be in the same direction. The only way this is possible is the friction force pointing to the right.

 

[BvU]

Yes, if the runner is trying to accelerate in the positive x direction (I didn't find that all too clearly in the story...). Runner pushes backward, exercises a force in the -x direction. No slipping means there must be a force in the +x direction to offset it: the friction force.

Compare with car braking: friction slows it down. Accelerating: friction allows it to accelerate.

 

[HalfLostAndSearching]

Yes, in this scenario, the friction force would point to the right in the direction of the positive x-axis. This is because the runner is moving to the right, and the friction force always acts in the opposite direction of the motion. Therefore, in order to accelerate to the right, the friction force must also point to the right.